A drive system for the closing movement of a multiaxial transport of workpieces in a transfer press is known from DE 199 14 652 C1. In this drive system, a dedicated drive with motion transfer means is assigned to the right-hand and left-hand gripper rail, so that the gripper rails are horizontally displaceable independently of each other. For the raising and lowering of the gripper rails, the drive system has a complex lifting mechanism, which extends almost over the entire width of the drive system and drives both gripper rails. Similarly, in a longitudinal movement in the direction of transport, the two gripper rails are jointly driven.